Answer:

Arcs and Inscribed Angles

Central angles are probably the angles most often associated with a circle, but by no means are they the only ones. Angles may be inscribed in the circumference of the circle or formed by intersecting chords and other lines.

Inscribed angle: In a circle, this is an angle formed by two chords with the vertex on the circle.

Intercepted arc: Corresponding to an angle, this is the portion of the circle that lies in the interior of the angle together with the endpoints of the arc.

Use two column proofs is easy to assert and prove the validity of a statement by writing formal arguments of mathematical statements. Also learn about paragraph and flow diagram proof formats.

Yes those are theorems, If two chords in a circle are congruent, then they determine two central angles that are congruent. If two chords in a circle are congruent, then their intercepted arcs are congruent. If two chords in a circle are congruent, then they are equidistant from the center of the circle.

Inscribed angles-

In geometry, an inscribed angle is the angle formed in the interior of a circle when two secant lines intersect on the circle. It can also be defined as the angle subtended at a point on the circle by two given points on the circle.

The inscribed angle θ is half of the central angle 2θ that subtends the same arc on the circle. Thus, the angle θ does not change as its vertex is moved around on the circle.

Equivalently, an inscribed angle is defined by two chords of the circle sharing an endpoint.

The inscribed angle theorem relates the measure of an inscribed angle to that of the central angle subtending the same arc.